Negative curves on blow-ups of weighted projective planes

In this website, you can search for negative curves on the blowup of weighted projective plane $\mathbb{P}(a,b,c)$ at a general nonsingular point, where $ a < b < c$ are pairwise coprime and $a, b, c <= 100$.

a (≤100)

b (≤100)

c (≤100)

Degree

Multiplicity

Only show: "No negative curve of deficiency 0 found"

Filter by (a+b+c)² ? a·b·c

This compares S² and abc, where S = a + b + c.

Order results by

Active filters: sorted by weights (asc)

Related search programs and code

This website accompanies the paper "Negative curves on blowups of weighted projective planes" and is based on several MAGMA programs. Place the files below in the same folder as this HTML file.

Riemann–Roch contributions: Contribution(r,[a,b]) and MakeCon(a,b,c) with examples, see Basic programs Con and MakeCon and more.txt .
Search for deficiency 0 curves: MAGMA program for negative curves of deficiency 0 for 0 < a < b < c ≤ 100, see Searching program deficiency 0.txt (the data shown in the table come from this search).
Search for deficiency 1 curves: MAGMA program for deficiency 1 (and higher) curves in the same range, see Searching program for deficiency 1 and higher.txt .
Programs for Section 5 and Theorem 5.1: including Curve(m,\nu,a,b,c), see Programs associated to prop 5.1.txt .
Programs for Theorem 5.3: additional MAGMA code in Program associated to prop 5.3.txt .

Results

P[a,b,c]	Coprime?	Status	Degree	Mult.	Source file